# Part C: FH Income Group Robustness

Tests whether S×Z heterogeneity is a functional-form artifact of development level.

## Model Comparison

| Model | N | Countries | R² | ρ |
|-------|---|-----------|----|----|
| M5c: FH + S×Z (baseline) | 5,661 | 169 | 0.180 | 0.841 |
| M5c+income: FH + S×Z + income controls | 4,677 | 165 | 0.179 | 0.843 |
| M5c-low-income: FH + S×Z | 1,418 | 63 | 0.231 | 0.799 |
| M5c-middle-income: FH + S×Z | 1,543 | 73 | 0.199 | 0.877 |
| M5c-high-income: FH + S×Z | 1,743 | 64 | 0.170 | 0.821 |

## Key Coefficients

| Variable | Model | Coef | SE | p-value |
|----------|-------|------|----|---------|
| savings_gdp | M5c: FH + S×Z (baseline) | 0.2594*** | 0.0260 | 0.0000 |
| savings_gdp | M5c+income: FH + S×Z + income controls | 0.2331*** | 0.0287 | 0.0000 |
| savings_gdp | M5c-low-income: FH + S×Z | 0.3776*** | 0.1372 | 0.0060 |
| savings_gdp | M5c-middle-income: FH + S×Z | 0.3547*** | 0.0512 | 0.0000 |
| savings_gdp | M5c-high-income: FH + S×Z | 0.1514*** | 0.0269 | 0.0000 |
| savings_x_Z1 | M5c: FH + S×Z (baseline) | 2.3185*** | 0.2848 | 0.0000 |
| savings_x_Z1 | M5c+income: FH + S×Z + income controls | 2.1861*** | 0.3099 | 0.0000 |
| savings_x_Z1 | M5c-low-income: FH + S×Z | 2.4877*** | 0.6452 | 0.0001 |
| savings_x_Z1 | M5c-middle-income: FH + S×Z | -0.0770 | 0.8579 | 0.9285 |
| savings_x_Z1 | M5c-high-income: FH + S×Z | 1.3815*** | 0.4079 | 0.0007 |
| savings_x_Z2 | M5c: FH + S×Z (baseline) | -0.3970*** | 0.0422 | 0.0000 |
| savings_x_Z2 | M5c+income: FH + S×Z + income controls | -0.3821*** | 0.0453 | 0.0000 |
| savings_x_Z2 | M5c-low-income: FH + S×Z | -0.4025*** | 0.1025 | 0.0001 |
| savings_x_Z2 | M5c-middle-income: FH + S×Z | -0.0195 | 0.1305 | 0.8814 |
| savings_x_Z2 | M5c-high-income: FH + S×Z | -0.2123*** | 0.0605 | 0.0005 |
| savings_x_Z3 | M5c: FH + S×Z (baseline) | 0.0178*** | 0.0017 | 0.0000 |
| savings_x_Z3 | M5c+income: FH + S×Z + income controls | 0.0173*** | 0.0018 | 0.0000 |
| savings_x_Z3 | M5c-low-income: FH + S×Z | 0.0175*** | 0.0044 | 0.0001 |
| savings_x_Z3 | M5c-middle-income: FH + S×Z | 0.0021 | 0.0054 | 0.7021 |
| savings_x_Z3 | M5c-high-income: FH + S×Z | 0.0091*** | 0.0024 | 0.0002 |